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1
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100%
Major J.
Didactica Mathematicae
|
2006
|
tom 29
|
nr 01
EN
The article contains no abstract
2
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Wokół twierdzenia Picka

64%
Major J., Major M.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2010
|
tom 3
117-140
PL
--
3
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Calculus without the concept of limit

64%
Błaszczyk P., Major J.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2014
|
tom 6
19-40
PL
There are two different approaches to nonstandard analysis: semantic(model-theoretic) and syntactic (axiomatic). Both of these approachesrequire some knowledge of mathematical logic. We present a method basedon an ultrapower construction which does not require any mathematical logicprerequisites. On the one hand, it is a complementary course to a standardcalculus course. On the other hand, since it relies on a different intuitivebackground, it provides an alternative approach. While in standard analysisan intuition of being close is represented by the notion of limit, in nonstandardanalysis it finds its expression in the relation is infinitely close. Asa result, while standard courses focus on the " − technique, we explorean algebra of infinitesimals. In this paper, we offer a proof of the theoremon the equivalency of limits and infinitesimals, showing that calculus can bedeveloped without the concept of limit.
4
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Z badań nad analizą rysunku i odkrywaniem własności funkcji

64%
Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2013
|
tom 5
95-104
PL
The article presents remarks regarding analysis of drawings and the use of the data contained therein in resolving mathematical tasks. A particular type of drawing is considered, which is a graph of a function. The presented findings are the result of several years of research conducted among the Mathematics students at the Pedagogical University of Cracow.
5
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Uwagi dotyczące pojęcia wartości bezwzględnej liczby rzeczywistej

64%
Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2006
|
tom 1
163-185
PL
This paper deals with some studies of understanding the absolute value of real numbers. This article is divided into two parts. The first one contains the conclusions drawn from the analysis of the solutions of the mathematical problems with the absolute value which were solved by the secondary school pupils. The second part of the article contains the didactic proposition of teaching the concept of absolute value at various levels of mathematical education.
6
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Remarks on the Sixteenth Slovak-Polish-Czech Mathematical School, IMEM Congress and the Seventh Nitrianska Mathematical Conference

64%
Major J., Major M.
Didactica Mathematicae
|
2009
|
tom 32
EN
Remarks on the Sixteenth Slovak-Polish-Czech Mathematical School, IMEM Congress and the Seventh Nitrianska Mathematical Conference
7
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Przyczynek do badań nad twórczą postawą studentów podczas rozwiązywania zadań matematycznych

64%
Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2012
|
tom 4
101-112
PL
In this paper, we understand the term ''creative attitude'' to denote an action of the learner which consists in undertaking creative activity. This activity can take different forms, such as: discovery, invention, a creative act, etc. We understand  ''discovery'' to denote a fact which already exists but was unknown to the discoverer. While teaching mathematics, we deal with such an understanding of  ''discovery'' e.g. when we use the problem method. Thence, subjectively new theorems can emerge during the solving of a mathematical problem by a student. Analyzing the collected research material, we try to determine the ability of students to find various regularities, which arise while solving mathematical problems, and to formulate these regularities in the form of theorems. We also pay attention to errors made by the respondents. The results of these observations may be helpful in assessing various aspects of mathematical activity of the examined individuals.
8
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Wybrane uwagi na temat roli zadań matematycznych w procesie nauczania-uczenia się matematyki

52%
Major J., Olik-Pawlik B., Ratusiński T., Zaręba L.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2016
|
tom 8
101-118
PL
The paper presents the comments relating to the role of tasks in theprocess of teaching and learning of mathematics in the context of educationof students studying to become teachers. In the considerations part, referencewas made to the fragments of undergraduate and postgraduate works, madeat seminars of didactics of mathematics.
9
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O roli prac dyplomowych z dydaktyki matematyki w kształceniu przyszłych nauczycieli matematyki

52%
Major J., Olik-Pawlik B., Ratusiński T., Zaręba L.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2017
|
tom 9
111-138
EN
In the training process of students – future teachers of mathematics, an important role is played by, among others, participation in the diploma seminar, during which the student (being at the final stage of studies)is tasked with preparing a bachelor’s or master’s thesis. This dissertation may be purely mathematical in nature or refer to problems in didactics of mathematics. The article aims to develop and illustrate some thoughts from previous works of the authors (Zaręba, 2009; Major, Olik-Pawlik, Ratusiński, Zaręba, 2016), pointing to the legitimacy of the preparation of teacher diploma theses in the field of didactics of mathematics by students.
10
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Z badań nad sylwetką absolwenta matematycznych studiów w Akademii Pedagogicznej w Krakowie w latach 2001-2007

52%
Ciesielska D., Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2009
|
tom 2
37-50
PL
The main goal of our studies was eliciting the opinion of graduates and students of the last year of Master studies on the course for teachers of mathematics at the Pedagogical University of Cracow. The research method was a survey questionnaire.We were interested in opinions on the level of studies at the college, and professional skills acquired in the study process. Moreover, we asked the questions concerning the professional career.In the article we present the analysis of the replies of respondents to the questions of the evaluation questionnaire form.
11
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O różnych sposobach definiowania wartość bezwzględnej

52%
Chronowski A., Major J., Powązka Z.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2009
|
tom 2
29-36
PL
In this article we present some didactic ideas of introducing theabsolute value of a real number by means of functional equations and aninequality. The basic properties of the absolute value of a real number arewritten as functional equations and an inequality. The function "absolutevalue" is a solution of a suitable functional equation or an inequality.
12
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Remarks on the Fifteenth Slovak-Polish-Czech Mathematical School and the Sixth Nitrianska Mathematical Conference

52%
Major J., Major M., Powązka Z.
Didactica Mathematicae
|
2008
|
tom 31
PL
The article summarises the Fifteenth Polish-Czech-Slovak Mathematical School and the Sixth Nitrianska Mathematical Conference (Nitrianska matematicka konferencja) - the meetings of Polish, Czech and Slovak mathematicians and mathematics teachers that took place this year.
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